The critical steering angle that the self-centering of the steering wheel occurs is one of the important measures for steering maneuverability. It is shown that this critical angle is influenced by the damping coefficient of the torsion bar if slight steering torque is applied just before releasing the steering wheel. Meanwhile, torque assistance device equipped vehicle generates assistance torque based on the deflection angle of torsion bar. Hence, the exceedingly high damping coefficient may cause deterioration of the assistance torque. Analytical results on the adequate range of the damping coefficient in view of both assistance torque and self-centering is shown.